Problem: Simplify the following expression: $ n = \dfrac{-5}{3} - \dfrac{-3y + 4}{-6} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-6}{-6}$ $ \dfrac{-5}{3} \times \dfrac{-6}{-6} = \dfrac{30}{-18} $ Multiply the second expression by $\dfrac{3}{3}$ $ \dfrac{-3y + 4}{-6} \times \dfrac{3}{3} = \dfrac{-9y + 12}{-18} $ Therefore $ n = \dfrac{30}{-18} - \dfrac{-9y + 12}{-18} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{30 - (-9y + 12) }{-18} $ Distribute the negative sign: $n = \dfrac{30 + 9y - 12}{-18}$ $n = \dfrac{9y + 18}{-18}$ Simplify the expression by dividing the numerator and denominator by -9: $n = \dfrac{-y - 2}{2}$